Positivity in Multifield Effective Field Theories.

Xu Li,Cen Zhang,Hao Xu,Chengjie Yang,Shuang-Yong Zhou

doi:10.1103/physrevlett.127.121601

Abstract

We discuss the general method for obtaining full positivity bounds on multifield effective field theories (EFTs). While the leading order forward positivity bounds are commonly derived from the elastic scattering of two (superposed) external states, we show that, for a generic EFT containing three or more low-energy modes, this approach only gives incomplete bounds. We then identify the allowed parameter space as the dual to a spectrahedron, constructed from crossing symmetries of the amplitude, and show that finding the optimal bounds for a given number of modes is equivalent to a geometric problem: finding the extremal rays of a spectrahedron. We show how this is done analytically for simple cases and numerically formulated as semidefinite programming (SDP) problems for more complicated cases. We demonstrate this approach with a number of well-motivated examples in particle physics and cosmology, including EFTs of scalars, vectors, fermions, and gravitons. In all these cases, we find that the SDP approach leads to results that either improve the previous ones or are completely new. We also find that the SDP approach is numerically much more efficient.

Highlights

[63] CMS Collaboration, Measurements of production cross sections of same-sign WW and WZ boson pairs in apssffisffio1⁄4cia1t3ionTewVi,thPhtyws.o jets Lett
While the leading order forward positivity bounds are commonly derived from the elastic scattering of two external states, we show that, for a generic effective field theories (EFTs) containing three or more low-energy modes, this approach only gives incomplete bounds
We demonstrate this approach with a number of well-motivated examples in particle physics and cosmology, including EFTs of scalars, vectors, fermions, and gravitons

Summary

Positivity in Multifield Effective Field Theories

Xu Li,1,* Hao Xu,2,3,† Chengjie Yang,1,‡ Cen Zhang,1,4,§ and Shuang-Yong Zhou 2,3,∥. We discuss the general method for obtaining full positivity bounds on multifield effective field theories (EFTs). We identify the allowed parameter space as the dual to a spectrahedron, constructed from crossing symmetries of the amplitude, and show that finding the optimal bounds for a given number of modes is equivalent to a geometric problem: finding the extremal rays of a spectrahedron. We show how this is done analytically for simple cases and numerically formulated as semidefinite programming (SDP) problems for more complicated cases. We shall consider the t → 0 limit of a two-to-two amplitude, Mij→klðsÞ 1⁄4 Mij→klðs; t 1⁄4 0Þ, which is only a function of s, and we define the M tensor

Published by the American Physical Society

Findings

Ciijj þ